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You are right about the history, though I was specifically talking about the usage of the word "number" not about whether people knew about fractions. I won't d
by ivan_ah 14y ago
You are right about the history, though I was specifically talking about the usage of the word "number" not about whether people knew about fractions. I won't dig up the reference, now, but I read in a history of Calculus treatise somewhere that Newton was the first who started using the word "number" in its present sense: any quantity including integers, rationals or irrationals.
Thx for spotting the f(x-h) typo. Fixed.
- blinkingled 14y agoIf a complete copy of the pdf is not available you might want to make a draft wip copy available for purchase. If the feedback in this thread is any indication I think a lot of good will come out of it. (You may also want to honor Knuth by paying people who bought the wip pdf and spotted mistakes :)
- mturmon 14y agoThis historical issue about the nature of a "number" also caught my eye. (In the PDF: "Before Newton, the word number referred only to the natural numbers...".) Of course, the notion of irrational numbers dates (at least) back to the classical Greeks (the proof-by-contradiction that root-2 is irrational is ancient and elementary, and will be known to some of your intended audience). In the Greek era, there was debate about the status of the irrationals, but sophisticated Greeks were well-acquainted with rational numbers. The statement in the PDF seems to ignore this. Summary: I think this statement of yours is dubious to begin with, and in any event would have to be so qualified and referenced that its value to a novice is nil.